New 3D Inverse Navier-Stokes Based Method Used to Design Turbomachinery Blade Rows

Present paper contains a method of solution of inverse problem for Navier-Stokes equations for 3D flows without any simplification of the problem statement and applied to design of turbomachinery bladed rows. In the developed method blade surface is impermeable and no-slip or any other boundary condition compatible with Navier-Stokes equations is applied on the blade surface. Solution of inverse problem is determined using moving grid, which is re-generated at each step of time-marching procedure (variation of flow-rate, impulse and energy fluxes due to movement of grid nodes is taken into account). Normal speed of face of grid cell adjacent to blade surface is determined using given static pressure (inverse mode) with the aid of relationships which are the elements of Godunov scheme applied for integration of flow equations.